Question

lf $w=\frac{z}{z-\frac{i}{3}}$ and $|w|=1,$ then z lies on

• A. a ellipse
• B. a circle
• C. a straight line
• D. a parabola

Answer 1

Answer: (C)

Given, $w=\frac{z}{z-\frac{i}{3}}$ and $|w|=1$
$\left|\frac{z}{z-\frac{i}{3}}\right|=1\Rightarrow |z|=\left|z-\frac{i}{3}\right|$
z lies on the perpendicular bisector of the line joining the points (0, 0) and (0, 1/3). So, z lies on a line.